Semi‐Implicit Euler Discrete‐Time Implementation of Fast Terminal Sliding Mode Control for Second‐Order Systems

This paper presents a semi‐implicit method for the digital implementation of a fast terminal sliding mode (FTSM) controller for second‐order systems. The proposed approach enables chattering‐free realization of FTSM control while achieving reduced computational cost and improved tracking accuracy, compared with the reported implicit method. Using the developed controller, the resultant closed‐loop dynamics are locally asymptotically stable at the origin and retain the hyperexponential convergence rate in its vicinity. Simulation results are provided to demonstrate the effectiveness of the proposed semi‐implicit controller.